QUESTION 4 The area bounded by the curves y = ²+1 and y =I+1 from intersection point to intersection point is rotated around y = 2. Find the vohume of the solid of revolution which is obtianed from this rotation.

Q: Question 4 Evaluate fVdr which V given by V = xy + 2xy + yz between A(0,0,0) and B(2,1,3) along the…

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Q: Question 7 Evaluate the triple by using cylindrical coordinates. ++y)dzdydx

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Q: Problem 4 B Find, by using polar coordinates in R?, the volume of the region bounded above by the…

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Q: Question 4. Calculate the arc length of the polar curve r = a(1 – cos 0).

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Q: Below is an arc of the astroid curve æ2/3 +y2/3 = 1, with exactly = 1.125 units of length. Note that…

A: Since you've asked multiple questions as per the answering guidelines we are supposed to answer the…

Q: Problem 2. Find the value of a > 0 such that the cone 22 = x² + y?, z > 0 is orthogonal to the…

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Q: Question 11 Calculate the surface area of the given surface. The parabolic cylinder with equation z…

A: Given: The parabolic cylinder lies over the triangle in the xy-plane with vertices (0,0),(0,4) and…

Q: Mw.3 Find Ih arcon regian for the ollowwg Regian bomdel.by.y=x- Y= and S=2

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Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. . 1. y =…

A: Surface area is 7✓55 π

Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. 2. y = ,…

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Q: Question 9. A circular helix in ryz-space has the following parametric equations, where 0 E R. r(0)…

A: Given: xθ=4cosθ, yθ=4sinθ and zθ=3θ The parametric equation of helix is rθ=4cosθ, 4sinθ, 3θ…

Q: Let the polar coordinate system be changed (for this problem only) by the introduction of a factor 2…

A: The solution are next step

Q: Question 4 Use polar coordinates to find the volume of the solid under the paraboloid z =x+y² and…

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Q: Question 9. A circular helix in ryz-space has the following parametric equations, where 0 ER. r(0) =…

A: Here,  xθ=4cosθyθ=4sinθzθ=3θ

Q: Problem 1.3. Make a 3D model for the solid that lies under the surface z =1-4x² y? and over the unit…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Question 9. A circular helix in xyz-space has the following parametric equations, where 0 E R. 4 cos…

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Q: Question 21 Consider the region in the third quadrant between the circles a² + y² = 4 and a² + y²…

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Q: Problem 1: Use spherical coordinates to evaluate the integral of Vr2+ y? + z2 over the ball of…

A: Since you have posted multiple question we are supposed to be answer only first one... kindly repost…

Q: Question (1): The arc of the parabola y = x2 from (1,1) to (2,4) is rotated about y-axis. Find the…

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Q: Problem 11 (i) Find the area bounded by the polar curves r = 0 + 1, r = 0+3, 0=0, and 0 = 2 (ii)…

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Q: QUESTION 1 (a) Calculate the area of the region between the graphs of f (x) = 2x^2 + 3x and g (x) =…

A: Note: There are multiple questions. No specific question has been asked. So, We will solve the first…

Q: 33. (a) Show that the total arc length of the ellipse x = 2 cos t, y = sint (0 <t< 27) is given by…

A: Given: x=2cost  , y=sint   0≤t≤2π To show : The length of total arc is  4∫0π21+3sin2tdt

Q: Question 1 Use polar coordinates to find the volume of the solid inside the cylinder x+y =9 and the…

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Q: Question 11 Let C be the path given by the parametriç equations Xt and y -1from t=0 to t=2 and let…

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Q: Question 3. The parametrized curve x = cos(t) – 5sin(t), %3D 101 y = -10cos(t)+ sin(t) is an…

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Q: Question 15 Using the change of coordinate system, the integral (z² + y²) dydæ would then take the…

A: Here we have to change the coordinate system.

Q: following equation aU (1,1). TC with U (0,t)= 0, = 0, and U (x,0)= sin 2. %3D %3D %3D at

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Q: Consider the ellipse 9 x + 4 y = 36 a) A parametrization of this ellipse is r(t)= ( 2 cos t, 3'sin…

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Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1

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Q: QUESTION 14 The equation of the tangent plane to z=f(xy) =x² siny at the point (1,0,0) is given by…

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Q: (a) The associated parametric curve is one-half of what familar conic? Sketch the exact curve. r (t)…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question...…

Q: Question 14 Find the area of the surface that is generated by revolving the portion of the curve y=…

A: Given: y=x2⇒x= ±y Since , we are dealing with x=1 to x=2, we will take the positive value Thus, x=y…

Q: QUESTION 11 A three-dimensional solid obtained by revolving a region in the xy-plane about a line is…

A: We have to check

Q: Page 9 9. The curve y = x2 with 0Sx<1 is rotated about the y-axis. Find the exact area of the…

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Q: Question 8 Calculate the area of the surface generated when the curve, y = Vx is revolved on the…

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Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. 2. y = ,…

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Q: (a) æ = sin t, y = csc t, 0 1. Thus, the curve is the portion of the hyperbola y = 1/x with y > 1.…

A: Given x=sin ty=csc t0&lt;t&lt;π2

Q: Question 7 Evaluate the triple by using cylindrical coordinates. LL x²+y)dzdydx

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Q: QUESTION 14 Which one of the following points lies on the curve r= sin 0-5. (5, 0) o (5, 2n) o (-5,…

A: In this we find that point which lies on the given curve.

Q: Question 9. A circular helix in xyz-space has the following parametric equations, where 0 E R. 4 cos…

A: The given parametric equations are, x(θ)=4cosθy(θ)=4sinθz(θ)=3θ Given, arclength of the helix is…

Q: Question 7 Calculate the area of the surface generated when the curve, f(x) = x³/2 . x1/2 on [1,2 ]…

A: Here f(x)= x32-x123 on the interval [1,2]it is revolving about the x-axis .The surface…

Q: Question 4 of 10 To describe a solid in geometry, it suffices to have two dimensions. O A. True OB.…

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Q: Question 5 of 5 Find the area of the surface of revolution generated by revolving the curve y = 3/a,…

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Q: Question 1 Find a normal vector and derite a parametric representation of the cylinder of revolution…

A: To find- Find a normal vector and derive a parametric representation of the cylinder of revolution

Q: Question 2 Let D1 be the solid in space that lies in the first octant x, y, z > 0, and be- tween the…

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Q: The area of the rotational surface resulting from rotating the arc of the curve x=cos^3 t, y=sin^3 t…

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Q: x = 7 cos 0 y = 14 sin 0 0 <0< 2n

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